SocialNetworks

CollaborationNetworksPaulErdős wasaHungarianmathematicianandoneofthemostprolificofthe20th century.Hehadmorethan500collaborators!

Erdős number=1 Erdős number=4

CollaborationNetworks

RichardBertram

JohnRinzel

WilfredRall

JohnEccles

ArthurSherman

CharlesPeskin

PeterLaxNobelPrize(1963) AbelPrize(2005)

BriefHistoryoftheStudyofSocialNetworks

JacobMoreno(1889-1974)

RomanianimmigranttotheU.S.whostudiedgroupinteractions.PublishedWhoShallSurvive?in1934,whichwasthefirstexamplepublishedexampleofsocialnetworkanalysis.

Hestartedthefieldofsociometry,nowcalledsocialnetworkanalysis,whichusesabstractnetworksandpropertiesofthesenetworkstostudysocialinteractions.Hecalledthenetworkssociograms.

BriefHistoryoftheStudyofSocialNetworks

FromWhoShallSurvive?

Friendshipnetworkbetweenaclassofschoolchildren.Triangles=boys,Circles=girls.

Doesthisnetworkdiagram,orsociogram,leadtoanyinsights?

BoysandGirlsLiveinDifferentWorlds

FromWhoShallSurvive?

Friendshipnetworkbetweenaclassofschoolchildren.Triangles=boys,Circles=girls.

Onecomponent:CangetfromoneVertextoanyother

Anothercomponent

BoysandGirlsLiveinDifferentWorlds

FromWhoShallSurvive?

Friendshipnetworkbetweenaclassofschoolchildren.Triangles=boys,Circles=girls.

A2-core:Eachvertexconnectedtoatleast2verticesinthesubset

Another2-core

A1-core

SomeKidsAreHubs

FromWhoShallSurvive?

Friendshipnetworkbetweenaclassofschoolchildren.Triangles=boys,Circles=girls.

Popularkidshavehighdegreecentrality

SomeKidsConnecttheTwoSubpopulations

FromWhoShallSurvive?

Friendshipnetworkbetweenaclassofschoolchildren.Triangles=boys,Circles=girls.

Thesekidshavehighbetweenness centrality

ShortestPathsBetweenKidsVaries,ButisUsuallyShort

FromWhoShallSurvive?

Friendshipnetworkbetweenaclassofschoolchildren.Triangles=boys,Circles=girls.

Thisisanexampleofasmall-worldnetwork

AffiliationNetworks

FromLuke(2015)

Exampleofabipartitenetworkinwhichtherearetwotypesofvertices:The“actors”connecttothe“groups”,buttherearenoactor-actororgroup-groupconnections

HowDoesOneAcquiretheInformationforaSocialNetwork?

Interviewpeople

“Whoareyourfriends?”afreechoicestudy

“WhoareyourfriendsatFSU?”restrictedtogeographiclocation

“Whoareyour10closestfriends?”afixedchoicestudy

Astudylikethisproducesadirectednetwork.Somedirectededgesbetweenverticesmaybebidirectional.

Limitations:timeconsumingwhatdoes“friend”mean?basedonanindividual’srecall

HowmanyacquaintancesdoesanaveragepersoninU.S.have? 2000

HowDoesOneAcquiretheInformationforaSocialNetwork?DirectObservation

DianFossey studiedgorillasocialnetworksinRwandafrom1966untilherdeath(probablymurder)in1985

JaneGoodallhasstudiedchimpanzeesocialnetworksfor55yearsinTanzania.StartedasasecretaryforLouisLeakey

HowDoesOneAcquiretheInformationforaSocialNetwork?ArchivalRecords

IntermarriagenetworkofrulingfamiliesofFlorencein15th century

HowDoesOneAcquiretheInformationforaSocialNetwork?ArchivalRecords

IntermarriagenetworkofrulingfamiliesofFlorencein15th century

networkhub

GettingNetworkInformationFromHiddenPopulations

TheDirectApproach

Telephoneinterview:“Howoftendoyouuseillegaldrugs?”

Questionproposedfor2020census:“AreyouaU.S.citizenorlegalimmigrant?”

AMoreEffectiveApproach

Snowballsampling:gaintrustofonepersonintargetpopulation,Theninvitethemtogivenamesofcontacts.Nextintervieweachofthese,gettingmorecontacts.Repeatuntilexhausted.Eachiterationiscalledasamplingwave.Thenumberofcontactsgrowsexponentiallywithnumberofwaves.

GettingNetworkInformationFromHiddenPopulations

AnEvenBetterApproachRandom-walksampling:Likesnowballsampling,butateachsteprandomlychooseonenewcontacttointerview,ratherthanallnewcontacts.

Advantageofrandom-walksampling:Thesamplesizegrowslinearlywithsamplingwaves,makingconvergencetoequilibriumstatisticsmuchmorerapidthanforsnowballsampling.

Atequilibrium,theprobabilityofbeinginterviewedisproportionaltothedegree(numberofedges)ofthecontact.

Thehigherthedegree,themorelikelythatthecontact isahiddenpopulation.

RandomWalk?

Randomwalkonagrid.Probabilitiesofbeingateachlocationgivenunbiasedselectionaregivenateachvertex.

UniversityofQueensland

WhereDoesSixDegreesofSeparationComeFrom?

SocialpsychologistStanleyMilgramconductedaseriesof“small-worldexperiments”inthe1960s.

Randomlymail96packages,or“passports”torecipientsinOmaha,Nebraska.

AskeachrecipienttogetthepassporttoafriendofMilgram’swholivedinBoston.Providename,location,andoccupation.

Butdon’tsenditdirectlytohim.Canonlysendthepassporttoafriendwhoyouthinkhasthebestchanceofgettingittothetarget.

Therecipientprovideshis/herownname/location,andmustthenfollowthesamedirections.

Onlysomeonewhoknowsthetargetcansendthepassportdirectlytothetarget.

WhereDoesSixDegreesofSeparationComeFrom?

Thepathlengthfromstartingpointtoendpointisequaltothenumberofnamesinthepassportonceitarrivestothetarget.

Atotalof18passportsarrivedtothetarget.Whatwastheaveragepathlength? 5.9

Similar,andwithgreatersamplesize,experimentshavebeenperformedsincethen.Allgivevaluescloseto6.Thus,average6degreesofseparationfrom2randomlychosenindividualsintheworld.

AlmostcertainlylessifrestrictedtoonelocationlikeTallahassee.Weliveinasmall(social)world.

JoeSchmo,TuscanLindaLight,NewOrleansWendyWing,BostonLouBlue,NewYorkRayDay,Boston

StanleyMilgramisMostFamousforHisObedienceExperimentsatHarvard?

In Milgram's basic paradigm, a subject walks into a laboratory believing that s/he is about to take part in a study of memory and learning. After being assigned the role of a teacher, the subject is asked to teach word associations to a fellow subject (who in reality is a collaborator of the experimenter). The teaching method, however, is unconventional—administering increasingly higher electric shocks to the learner. Once the presumed shock level reaches a certain point, the subject is thrown into a conflict. On the one hand, the strapped learner demands to be set free, he appears to suffer pain, and going all the way may pose a risk to his health. On the other hand, the experimenter, if asked, insists that the experiment is not as unhealthy as it appears to be, and that the teacher must go on. In sharp contrast to the expectations of professionals and laymen alike, some 65% of all subjects continue to administer shocks up to the very highest levels.

FromanarticleinAmericanPsychologist(1990):

KevinBacon

TheRiverWild(1994)

MysticRiver(2003)

Footloose(1984)

Apollo13(1995)

Flatliners (1990) PatriotsDay(2016)

SixDegreesofKevinBaconBaconin1994interview:“IhaveworkedwitheveryoneinHollywoodorsomeonewhohasworkedwiththem”

SixDegreesofKevinBaconBaconin1994interview:“IhaveworkedwitheveryoneinHollywoodorsomeonewhohasworkedwiththem”

MotivatedfourcollegestudentsatAlbrightCollegetocreateanetworkofthosewhohavebeeninmovieswithBacon,orthosewhohavebeeninmovieswiththem

SixDegreesofKevinBaconBaconin1994interview:“IhaveworkedwitheveryoneinHollywoodorsomeonewhohasworkedwiththem”

MotivatedfourcollegestudentsatAlbrightCollegetocreateanetworkofthosewhohavebeeninmovieswithBacon,orthosewhohavebeeninmovieswiththem

KevinBacon

LeVarBurton

PatrickStewart

MaryTylerMoore

RoseanneBarr

ElvisPresley

AnnMargret

EdAsner

Baconnumber=0

Baconnumber=1

Baconnumber=2

Baconnumber=3

Hypothesis: AllcurrentmajoractorsinHollywoodhaveBaconnumber6orlower

WhatAboutFacebookandOtherSocialMedia?

Lotsofdata,butfewstudies.Reasonisthatthesedataareproprietary.

Butitiscertainthatthecompaniesthemselvesemploypeopletoanalyzetheirsocialnetworkdata.

TheEnd